Where should computer simulations be located on the ‘usual methodological map’ which distinguishes experiment from theory? Specifically, do simulations ultimately qualify as experiments or as thought experiments? Ever since Galison raised that question, a passionate debate has developed, pushing many issues to the forefront of discussions concerning the epistemology and methodology of computer simulation. This review article illuminates the positions in that debate, evaluates the discourse and gives an outlook on questions that have not yet been addressed.